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From |
Dirk Enzmann <dirk.enzmann@uni-hamburg.de> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Re: correct confidence intervals of -mean- ? |

Date |
Sat, 06 Mar 2010 15:01:10 +0100 |

Kit,

Dirk Kit Baum wrote: > Dirk said > > Very carefully I want to ask: Are the confidence intervals given by > -mean- really correct? > > Below I compare the results of -mean- with the results of a different > procedure: > > and goes on to show that -mean- CIs can be reproduced by collapsing, > but maintaining the DF in the confidence interval as that of the whole > sample. These are the same standard errors of mean reported by > > tabstat price,by(rep78) stat(mean sd n semean) > > He wonders whether the DF used in calculating s.e.(mean) should be > that of the full sample. I think that -mean- and -tabstat- are both > using the notion that you have a model y = mu + \epsilon, where > var(\epsilon} is a population parameter. Thus the variance of \epsilon > is a constant for all subsamples, and when you calculate s.e. mean, > you use the sqrt of that common variance and divide by the sqrt(sample > size) of the subpopulation. You can see that is being done by > -tabstat- by comparing the sd, n and semean columns. > > What does surprise me is that the CIs generated by these methods > differ so widely from those computed by > > reg price i.rep78 > margins rep78 > > The differences are not just a small-sample/large-sample adjustment of > the Root MSE. If you take apart the VCE of a regression of price on > all five dummies, no constant term, you find a diagonal matrix > containing the inverses of the respective sample sizes, so the > difference has to lie in the computation of \hat{sigma^2} which > multiplies inv(X'X). ************************************************* Dr. Dirk Enzmann Institute of Criminal Sciences Dept. of Criminology Schlueterstr. 28 D-20146 Hamburg Germany phone: +49-(0)40-42838.7498 (office) +49-(0)40-42838.4591 (Mrs Billon) fax: +49-(0)40-42838.2344 email: dirk.enzmann@uni-hamburg.de

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**References**:**st: correct confidence intervals of -mean- ?***From:*Dirk Enzmann <dirk.enzmann@uni-hamburg.de>

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